The Weil conjectures in the special case of algebraic curves were conjectured by.

Weil realized that to prove such a connection one needed a new cohomology theory, but neither he nor any other expert saw how to do this until such a theory was found by Grothendieck.

For drivers, the main route through the region is the rapid A 5 ( E35 ) motorway, but a variety of sign-posted scenic routes such as the Schwarzwaldhochstraße (, Baden-Baden to Freudenstadt ), Schwarzwald Tälerstraße (, the Murg and Kinzig valleys ) or Badische Weinstraße ( Baden Wine Street,, a wine route from Baden-Baden to Weil am Rhein ) offers calmer driving along high roads.

With less time to spend songwriting as she focused on a burgeoning film career, during the early 1980s Parton recorded a larger percentage of material from noted pop songwriters, such as Barry Mann and Cynthia Weil, Rupert Holmes, Gary Portnoy and Carole Bayer Sager.

Recently, a large number of cryptographic primitives based on bilinear mappings on various elliptic curve groups, such as the Weil and Tate pairings, have been introduced.

The songs on the album were written by such people as Tony Romeo, Terry Cashman, Tommy West, Barry Mann, and Cynthia Weil.

) It contained a few cover versions of some classic songs such as " Walking in the Rain " written by Barry Mann, Cynthia Weil, and Phil Spector.

According to several Weil scholars such as Eva Fogelman and Robert Coles, this experience may well be related to the exceptionally strong altruism displayed throughout her life.

With the Melos Ensemble he recorded chamber music for both woodwinds and strings, such as Ravel's Introduction and Allegro along with Osian Ellis ( harp ), Gervase de Peyer ( clarinet ), Emanuel Hurwitz and Ivor McMahon ( violin ), Cecil Aronowitz ( viola ) and Terence Weil ( cello ).

To see the relation of these sets to the Weil conjectures, notice that if α and are both in, then there exist x and y in Z / pZ such that x < sup > 3 </ sup > = α and y < sup > 3 </ sup > = α + 1 ; consequently, x < sup > 3 </ sup > + 1 = y < sup > 3 </ sup >.

It is also easy to prove the Weil conjectures for other spaces, such as Grassmannians and flag varieties, which have the same " paving " property.

In practice it is this generalization rather than the original Weil conjectures that is mostly used in applications, such as the hard Lefschetz theorem.

After his return, there were heated arguments with authors such as Jiří Weil and Jan Slavik, who criticized developments under Joseph Stalin.

The most efficient identity-based encryption schemes are currently based on bilinear pairings on elliptic curves, such as the Weil or Tate pairings.

This has many applications, such as the proof of the Weil conjectures and the construction of representations of finite groups of Lie type.

( One reason for this is that Weil suggested that the Weil conjectures could be proved using such a cohomology theory.

The general idea is that one motive has the same structure in any reasonable cohomology theory with good formal properties ; in particular, any Weil cohomology theory will have such properties.

Pupils such as Avigdor Arikha, Naftali Bezem, Shraga Weil and Shmuel Boneh absorbed these influences and integrated them into their later work.

Sage Weil developed such a script in May 1994.

A study by Kirchner and Anne Weil showed that the time taken for life on earth to recover from extinction episodes such as that which destroyed the dinosaurs is not, as previously thought, proportional to the damage done.

It has served as the production entity for network shows on the ARD, such as Verbotene Liebe, which over the years has exposed many young actors to the German audience, such as Andreas Stenschke, Jo Weil, Luca Zamperoni and Kay Böger.

In relation with differential geometry ( Chern – Weil theory ) and the theory of Grassmannians, a much more hands-on approach to the theory is possible for cases such as the unitary groups that are of greatest interest.

In mathematics, the Weil conjectures were some highly-influential proposals by on the generating functions ( known as local zeta-functions ) derived from counting the number of points on algebraic varieties over finite fields.

The more strict analogy expressed by the ' global field ' idea, in which a Riemann surface's aspect as algebraic curve is mapped to curves defined over a finite field, was built up during the 1930s, culminating in the Riemann hypothesis for local zeta-functions settled by André Weil in 1940.

André Weil's famous Weil conjectures proposed that certain properties of equations with integral coefficients should be understood as geometric properties of the algebraic variety that they define.

Weil also showed that the conductor of the elliptic curve should be the level of the corresponding modular form.

Simone Weil who fought for the French resistance ( the Maquis ) argued in her final book The Need for Roots: Prelude to a Declaration of Duties Towards Mankind that for society to become more just and protective of liberty, obligations should take precedence over rights in moral and political philosophy and a spiritual awakening should occur in the conscience of most citizens, so that social obligations are viewed as fundamentally having a transcendent origin and a beneficent impact on human character when fulfilled.

The Hasse – Weil conjecture states that the Hasse – Weil zeta function should extend to a meromorphic function for all complex s, and should satisfy a functional equation similar to that of the Riemann zeta function.

Weil says that patients should take the Western medicine prescribed by the doctor, and then incorporate alternative therapies such as omega-3 fatty acids, vitamin D, and herbal remedies, meditation and other “ spiritual ” strategies.

It was then Weil realized he should not be communicating to this student in such a manner.

Robert Langlands argued in 1973 that the modern version of the should deal with Hasse – Weil zeta functions of Shimura varieties.

Weil was mistakenly arrested in Finland at the outbreak of the Winter War suspected of spying ; however, accounts of his life having been at danger have been shown to be exaggerated.

Mordell's theorem had an ad hoc proof ; Weil began the separation of the infinite descent argument into two types of structural approach, by means of height functions for sizing rational points, and by means of Galois cohomology, which was not to be clearly named as that for two more decades.

Grothendieck saw that it would be possible to use Serre's idea to define a cohomology theory which he suspected would be the Weil cohomology.

* As described by Ross, Weil & Roberson for Enterprise Architecture, consider letting the BI project be driven by other business initiatives with excellent business cases.

Because of the Mordell – Weil theorem, Faltings ' theorem can be reformulated as a statement about the intersection of a curve C with a finitely generated subgroup Γ of an abelian variety A. Generalizing by replacing C by an arbitrary subvariety of A and Γ by an arbitrary finite-rank subgroup of A leads to the Mordell – Lang conjecture, which has been proved.

Weil negotiated with the Ministry of Education that the Director of the Institute would be a full professor from the state system, so that the Institut would have the status of a University institution.

The first problem with this is that the coefficient field for a Weil cohomology theory cannot be the rational numbers.

The original Weil conjectures follow by taking f to be a morphism from a smooth projective variety to a point and considering the constant sheaf Q < sub > l </ sub > on the variety.

The terminology may be due to Weil, who wrote his Basic Number Theory ( 1967 ) in part to work out the parallelism.

These days these are associated to algebraic groups ( respectively the Weil restriction from a totally real number field of GL ( 2 ), and the symplectic group ), for which it happens that automorphic representations can be derived from analytic functions.

Étale cohomology theory can be used to construct ℓ-adic cohomology, which is an example of a Weil cohomology theory in algebraic geometry.

While the category of motives was supposed to be the universal Weil cohomology much discussed in the years 1960-1970, that hope for it remains unfulfilled.

In 1944, local landowner Lionel Weil, a founder of Goldsboro's historic Oheb Shalom synagogue and uncle of Gertrude Weil, proposed that the cliffs area along the Neuse River be preserved as a state park.

Also, we obtain the classical Borel – Weil theorem as a special case of this theorem by taking to be dominant and to be the identity element.

In section VII, article 358, Gauss proved what can be interpreted as the first non-trivial case of the Riemann Hypothesis for curves over finite fields ( the Hasse – Weil theorem ).

Lehman's attorney Harvey R. Miller of Weil, Gotshal & Manges, said " the purchase price for the real estate components of the deal would be $ 1. 29 billion, including $ 960 million for Lehman's New York headquarters and $ 330 million for two New Jersey data centers.